There have been rumors (perceived as threats) of Hollywood making a live-action Evangelion for about as long as the show itself has been around. I also remember hearing rumors of a live-action Sailor Moon starring Keanu Reeves as Tuxedo Mask back in the late 90's.
The Evangelion movie is basically dead. ADV barely has enough money to subtitle anime anymore. When you consider that subtitling anime is something fat college students do in their spare time, this casts some doubt on their ability to finance a special effects film.
Cameron just recently managed to pass off the biggest heap of worn cliches I've ever seen as "a revolutionary motion picture event," so if he wants Alita made I don't think any force can stop him.